Unique thermodynamic relationships for [Delta]fHo...

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Original citation: Vegas, Ángel, Liebman, Joel F. and Jenkins, H. Donald Brooke (2012) Unique thermodynamic relationships for Delta H-f(o) and Delta(f)G(o) for crystalline inorganic salts. I. Predicting the possible existence and synthesis of Na2SO2 and Na2SeO2. Acta Crystallographica Section B Structural Science, Vol.68 (No.5). pp. 511-527. Permanent WRAP url: http://wrap.warwick.ac.uk/50809 Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes the work of researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available. Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher’s statement: http://dx.doi.org/10.1107/S0108768112030686 A note on versions: The version presented in WRAP is the published version or, version of record, and may be cited as it appears here. For more information, please contact the WRAP Team at: [email protected]

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research papers

Acta Cryst. (2012). B68, 511–527 doi:10.1107/S0108768112030686 511

Acta Crystallographica Section B

StructuralScience

ISSN 0108-7681

Unique thermodynamic relationships for DfHo and

DfGo for crystalline inorganic salts. I. Predicting the

possible existence and synthesis of Na2SO2 andNa2SeO2

Angel Vegas,a,b Joel F. Liebmanc

and H. Donald Brooke Jenkinsd*

aUniversidad de Burgos, Parque Cientıfico y

Tecnologico, Edificio I+D+I, Plaza Misael

Banuelos, Burgos 09001, Spain, bInstituto de

Quımica Fısica ‘Rocasolano’, CSIC, Madrid,

Spain, cDepartment of Chemistry and Biochem-

istry, University of Maryland, Baltimore County,

Maryland 21250, USA, and dDepartment of

Chemistry, University of Warwick, Gibbet Hill

Road, Coventry CV4 7AL, England

Correspondence e-mail:

[email protected]

# 2012 International Union of Crystallography

Printed in Singapore – all rights reserved

The concept that equates oxidation and pressure has been

successfully utilized in explaining the structural changes

observed in the M2S subnets of M2SOx (x = 3, 4) compounds

(M = Na, K) when compared with the structures (room- and

high-pressure phases) of their parent M2S ‘alloy’ [Martınez-

Cruz et al. (1994), J. Solid State Chem. 110, 397–398; Vegas

(2000), Crystallogr. Rev. 7, 189–286; Vegas et al. (2002), Solid

State Sci. 4, 1077–1081]. These structural changes suggest that

if M2SO2 would exist, its cation array might well have an anti-

CaF2 structure. On the other hand, in an analysis of the

existing thermodynamic data for M2S, M2SO3 and M2SO4 we

have identified, and report, a series of unique linear relation-

ships between the known �fHo and �fG

o values of the alkali

metal (M) sulfide (x = 0) and their oxyanion salts M2SOx (x = 3

and 4), and the similarly between M2S2 disulfide (x = 0) and

disulfur oxyanion salts M2S2Ox (x = 3, 4, 5, 6 and 7) and the

number of O atoms in their anions x. These linear relation-

ships appear to be unique to sulfur compounds and their

inherent simplicity permits us to interpolate thermochemical

data (�fHo) for as yet unprepared compounds, M2SO (x = 1)

and M2SO2 (x = 2). The excellent linearity indicates the

reliability of the interpolated data. Making use of the volume-

based thermodynamics, VBT [Jenkins et al. (1999), Inorg.

Chem. 38, 3609–3620], the values of the absolute entropies

were estimated and from them, the standard �fSo values, and

then the �fGo values of the salts. A tentative proposal is made

for the synthesis of Na2SO2 which involves bubbling SO2

through a solution of sodium in liquid ammonia. For this

attractive thermodynamic route, we estimate �Go to be

approximately �500 kJ mol�1. However, examination of the

stability of Na2SO2 raises doubts and Na2SeO2 emerges as a

more attractive target material. Its synthesis is likely to be

easier and it is stable to disproportionation into Na2S and

Na2SeO4. Like Na2SO2, this compound is predicted to have an

anti-CaF2 Na2Se subnet.

Received 21 May 2012

Accepted 5 July 2012

1. Introduction

Emerging in recent studies (see for example, Nalbandyan &

Novikova, 2012), is the usefulness of combining simple ther-

modynamic ideas (obtained by using volume-based thermo-

dynamics, VBT) with structural science concepts in order to

gain new insights into the structural characteristics of

condensed phases.

This present article bridges the topics of energetics (ther-

modynamics) and structural science, often using the VBT

approach in order to obtain the thermodynamics. This latter

procedure requires no structural details whatsoever (Glasser

& Jenkins, 2011a) and relies only on knowing the volume of

the formula unit involved. However, once combined with

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Vegas’ oxygen–pressure concept (Martınez-Cruz et al., 1994)

this enables the capability of VBT to be extended and struc-

tural details also can then emerge.

In 1994 Vegas and co-workers pointed out the equivalence

between oxidation and pressure (Martınez-Cruz et al., 1994).

That is to say that adding O atoms to a lattice during oxidation

creates an internal pressure within the lattice. This idea was

based on high-pressure (HP) experiments carried out by Beck

& Lederer (1993) on the BaSn alloy which at 3.5 GPa

underwent the B33 ! CsCl transition. It is well known that

cations in perovskites, like BaSnO3 (Pm�33), are also CsCl-type,

so that both HP-BaSn and BaSnO3 have a common pattern.

The important issue of this coincidence was that their simi-

larity was not only topological but that their unit-cell dimen-

sions were almost equal (4.07 and 4.11 A for BaSn and

BaSnO3). Thus, the evidence was that the insertion of three O

atoms into the B33 network of BaSn produced the same effect

as the application of a pressure of 3.5 GPa.

This concept which equates oxidation with the resultant

imposed internal pressure (caused by stuffing the O atoms into

the lattice) has been successfully utilized in order to explain –

in qualitative terms – the structural changes observed in the

cation substructures of many oxides when compared with the

structure of their parent ‘alloy’ (Martınez-Cruz et al., 1994;

Vegas, 2000; Vegas & Jansen, 2002). Among them, the system

Na2S/Na2SOx has received special attention with high-pres-

sure experiments being performed on Na2S (Vegas et al., 2001)

and with attendant crystal chemical studies of both the Na2S

phases and their corresponding existing oxides Na2SO3 and

Na2SO4 (Vegas & Garcıa-Baonza, 2007; Vegas, 2011). Such

studies showed the existence of a direct relationship between

the Na2S substructures and the oxygen contents of the

Na2SOX oxide, as well as discussing the opposing role (to

pressure) of temperature (where we see expansion of the

lattice) in determining the observed phase transitions. In the

case of Na2S, high-pressure experiments showed the double

transition CaF2 ! PbCl2 ! Ni2In (Vegas et al., 2001). A

further paper dealing with theoretical calculations on K/K2S/

K2SO4 has been published by Vegas & Mattesini (2010).

However, a comprehensive study including many alkali

sulfates and selenates (Vegas, 2011) suggests that the M2S

sulfides would follow the transition path 1 as a result of

successively increasing the external pressure.

Several of these binary phases correspond to one of the

observed Na2S substructures found within the known phases

of Na2SO3 and Na2SO4. Thus, in Na2SO3 the Na2S substruc-

ture is of the Ni2Al type, whereas in V-Na2SO4 (thenardite), it

has a TiSi2-type subarray at room temperature, transforming

at high temperature into the I-Na2SO4 phase, with a Na2S

subarray of the hexagonal Ni2In-type. The PbCl2 structure is

not found in any Na2SO4 phase, but it is present in the room-

temperature phase of the related K2SO4. Thus, in this way, a

higher O content stabilizes those phases which correspond to

higher-pressure phases. Within this scheme has been suggested

the possible existence of Na2SO2 sulfoxylate, whose lower O

content, in terms of the ‘oxidation–pressure’ concept, should

yield a structure closer to the room-pressure phase of Na2S

(i.e. the anti-CaF2-type structure of the parent Na2S). The

structure proposed for Na2SO2 is represented in Fig. 1. An

analogous situation is anticipated for Na2SeO2, which should

be much easier to synthesize.

Historically, one of us (AV) proposed the synthesis of

Na2SO2 to Martin Jansen, during a stay in Stuttgart in 2000.

Jansen has reported to us that the synthesis was attempted,

under his direction, by a Diploma student (Wiench, 1975) who

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512 Angel Vegas et al. � Unique thermodynamic relationships Acta Cryst. (2012). B68, 511–527

Figure 1Two perspective views of hypothetical Na2SO2 or the Na2SeO2 structures.(a) An anti-CaF2 structure formed by 2 Na atoms (green) and SO4 (orSeO4 tetrahedra) (S: yellow; O: red). The S(Se)O2 groups are representedas tetrahedral to indicate that the O atoms cannot be located. The SO4

tetrahedra should be taken as disordered SO2 groups. (b) The same anti-CaF2-type structure of Na2SO2 or Na2SeO2 showing the simple cubicarray of the Na atoms (green) alternately filled by the SO2 (or SeO2)groups (S: yellow; O: red). In turn, the S atoms (yellow) form a f.c.c. arraywhere all the tetrahedra are filled by the Na atoms. In this case, two Oatoms from the tetrahedra drawn in (a) have been deleted randomly toform the SO2 (or SeO2) groups. Their random orientation indicates thattheir positions are unpredictable and that in the cubic CaF2-type structure(Fm�33m) they must necessarily show positional disorder.

tried to obtain the compound by heating disodium peroxide

with sulfur, in a sealed ampoule under vacuum. This synthesis

route was unsuccessful and AV considered that a possible

reason for the failure to synthesize the material was because of

the high-temperature conditions employed. So in this present

article new synthetic routes at lower temperature are explored

making use of the magnitudes derived from the Jenkins VBT

approach (Jenkins et al., 1999; Jenkins, 2009; Glasser &

Jenkins, 2011b).

The stages required towards examining the feasibility of the

syntheses of sulfoxylates (and later disodium selenoxylate) are

first to identify a suitable synthetic route from both a practical

and a thermodynamic standpoint, and then to check on its

thermodynamic stability in respect of proneness to decompose

or disproportionate. The VBT theory (Jenkins et al., 1999;

Jenkins, 2009; Glasser & Jenkins, 2011b) appears to be the

appropriate tool to determine the stability of these

compounds in terms of their �fHo and �fG

o magnitudes. The

study will be extended to the whole family of oxysalts of the

formulae M2SOX (x = 1–4) and M2S2OX (x = 3–7). Disodium

selenoxylate, Na2SeO2, is given particular consideration.

Although likely synthesizable, the stability of disodium

sulfoxylate, Na2SO2, cannot be unequivocally established. The

stability of the dicaesium, Cs2SO2, and potassium salt, K2SO2,

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Acta Cryst. (2012). B68, 511–527 Angel Vegas et al. � Unique thermodynamic relationships 513

Table 1Equations of best fit for data in Table 2 using data from Wagman et al. (1982).

Column 6 lists the values of x for which experimental values (in Table 2) are available. In order to assess the errors in predicted values we can calculate thepredicted experimental values = Kx + C and compare these with the experimentally known value. (Predicted� experimental) is the magnitude of the error in eachof the values. We then quote the square root of the sum of the squares of these errors in the x = 0 and x = 3 values in column 8. This then approximates the errorscaused by interpolation for x = 1 and x = 2 for M2SOx salts. In the case of M2S2Ox salts the overall r.m.s. error is quoted in column 8. This may overestimate theinterpolation errors in most of these cases.

Item number M

K[kJ mol�1 (Oatom)�1] C (kJ mol�1)

Correlation coeffi-cient, R2

No. of points, N, xvalues Error (kJ mol�1)†

Average errors oninterpolation ofvalues (kJ mol�1)‡

Sulfoxylates1 �fH

o(Li2SOx,c) �248.0 �439.8 0.999 3 x = 0; �1.6 (0.4%) � 3.5x = 0, 3, 4 x = 3; 6.8 (0.6%)

x = 4; �4.7 (0.3%)2 �fH

o(Na2SOx,c) �253.2 �360.1 0.999 3 x = 0; �4.7 (1.3%) � 9.3x = 0, 3, 4 x = 3; 18.9 (1.7%)

x = 4;�14.2 (1.0%)3 �fG

o(Na2SOx,c) �228.0 �345.6 0.999 3 x = 0; �4.2 (1.2%) � 8.8x = 0, 3, 4 x = 3; 17.1 (1.7%)

x = 4;�12.6 (1.0%)4 �fH

o(Na2S2Ox,c) �215.1 �413.0 0.996 6 x = 0; 15.9 (4.0%) � 11.1x = 0, 3, 4, 5, 6, 7 x = 3;�64.7 (5.8%)

x = 4; 41.2 (3.3%)x = 5; 10.3 (0.7%)x = 6; 4.6 (0.3%)x = 7; �6.4 (0.3%)

5 �fGo(Na2S2Ox,c) �189.6 �406.9 0.997 4 x = 0; 28.2 (7.4%) � 14.9

x = 0, 3, 6, 7 x = 3;�52.3 (5.1%)x = 6; 12.5 (0.8%)x = 7; 11.8 (0.7%)

6 �fHo(K2SOx,c) �260.6 �373.3 0.998 3 x = 0; �7.4 (1.9%) � 10.1

x = 0, 3, 4 x = 3; 29.6 (2.6%)x = 4;�22.2 (1.5%)

7 �fGo(K2SOx,c) �239.1 �374.5 0.991 3 x = 0;�10.5 (2.9%) � 18.2

x = 0, 3, 4 x = 3; 53.8 (5.2%)x = 0; �9.5, (0.7%)

8 �fHo(K2S2Ox,c) �218.4 �459.2 0.997 5 x = 0; 27.0 (6.2%) � 13.0

x = 0, 3, 5, 6, 7 x = 3;�59.3 (5.0%)x = 5; 17.2 (1.1%)x = 6; 13.9 (0.8%)x = 7; 1.2 (0.1%)

9 �fHo(Rb2SOx,c) �268.7 �360.7 1.000 2 Only two points

availableNo error estimable

x = 0, 4

10 �fHo(Cs2SOx,c) �267.9 �354.2 0.999 3 x = 0; 5.8 (1.6%) � 8.0

x = 0, 3, 4 x = 3; 23.2 (2.0%)x = 4; 17.2 (1.2%)

Sodium selenoxylates11 �fH

o(Na2SeOx,c) 23.8x2� 277.2 x � 341.4§ 1.00 3 Only two points

availableNo error estimable

x = 0, 3, 4

† Error = ex = (predicted� actual) (kJ mol�1) and percentage error of prediction (%) for the cases (x) in which the experimental value is known. ‡ Average errors on interpolation ofvalues (kJ mol�1), e.g. between x = 0 and x = 3, error is 1

2(e02 + e3

2). In general they are: (1/n)(�ni = 0ei

2). § NB Not being a sulfur compound, a linear relationship needs to be replaced bya polynomial curve of degree 2 (quadratic) to form the basis of the fit for �fH

o(Na2SeOx,c) versus x.

however, seems established. Further we can predict, with

much more certainty, the existence (stability) of disodium

selenoxylate, Na2SeO2, and several suitably straightforward

and thermodynamically favoured synthetic routes for this

latter material.

2. Discussion

2.1. Trends in available thermodynamic data

In the normal run of things standard thermochemical data,

�fHo and �fG

o for a series of oxy salts, when plotted as a

function of the number of O atoms present, x, will show an

irregular variation. An example is shown in Fig. 2, where, for

the series of sodium and potassium ox salts based on chlorine,

NaClOx and KClOx (0 � x � 4), known standard enthalpy of

formation data �fHo (Wagman et al., 1982; Karapet’yants &

Karapet’yants, 1970) when plotted versus x leads to irregular

plots so making meaningful estimation of unknown inter-

mediate values of �fHo, say for x = 1 for (NaClO) and x = 1

and 2 for K (KClO and KClO2), virtually impossible. This

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Table 2Standard thermochemical data for the salts, M2SOx and M2S2Ox andM2SeOx in their crystalline (c) phases.

Literature (upright type): thermodynamic data (taken from Wagman et al.,1982, unless otherwise specified) and (in italics) predicted data from this study.Errors in this table are taken to be the r.m.s. of the sum of the errors found forthe known materials, e.g. error (kJ mol�1) found for �fH

o predicted forinterpolated Li2SO and Li2SO2 taken as�3.5 (from item 1, column 8, Table 1).

Compound �fHo (kJ mol�1) �fG

o (kJ mol�1) So298 (J K�1 mol�1)

SulfoxylatesLi2S �441.4 –439.084a† 63.6b

78 � 15c‡Li2S2 �438.1 – –Li2SO �688 � 7c§ �658 � 11c} 90 � 15c‡Li2SO2 �936 � 7c§ �878 � 11c} 102 � 15c‡Li2SO3 �1177.0 �1092 � 4c} 114 � 15c‡Li2SO4 �1436.49 �1321.77 115.1

�1436.489a�1321.58a

Na2S �364.8 �349.8 83.7�354.551a 97 � 2d

109 � 15c

Na2S2 �397.1 �378.7 105Na2SO �613 � 19c§ �574 � 18c§ 115 � 15c

Na2SO2 �867 � 24c§ �802 � 22c§ 121 � 15c

Na2SO3 �1100.8 �1012.5 145.94�1096.78 � 0.81e

�1012.326a 124 � 15c

�1101.8 � 0.7f

�1100.802a

Na2SO4 �1387.1 �1270.2 149.6�1387.816a

�1269.848a 136 � 15c

Na2S2O �628 � 79c§ –597 � 62c§ –Na2S2O2 �843 � 79§ –786 � 62§ –Na2S2O3 �1123.0 �1028.0 155Na2S2O4 �1232.2 – –Na2S2O5 �1478.2 �1354 � 62c§ –Na2S2O6 �1699.04 �1531.8g –Na2S2O7 �1925.1 �1722.1 202.1K2S �380.7 �364.0 104.6

�362.745a 124 � 15c

K2S2 �432.2 – –K2SO �634 � 31c§ �613 � 55c§ 154 � 15c

K2SO2 �895 � 31c§ �853 � 55c§ 156 � 15c

K2SO3 �1125.5 �1038.030a§ 159 � 15c

�1123.37 � 0.96e

K2SO4 �1437.79 �1321.43 175.6�1319.684a 159 � 15c

K2S2O �678 � 69c§ – –K2S2O2 �896 � 69c§ – –K2S2O3 �1173.6 – –K2S2O4 �1333 � 69c§ – –K2S2O5 �1533.9 – –K2S2O6 �1755.61 – –K2S2O7 �1986.6 �1791.6 255K2S2O8 �1916.1 �1697.41 278.7

�2182 � 69c – –Rb2S �360.7 �350 � 9c† 167 � 15c ‡

133.9b

150 � 15 averageRb2SO �629c§ �594 � 4c} 171 � 15c‡Rb2SO2 �898c§ �833 � 4c} 174 � 15c‡Rb2SO3 �1167c§ �1073� 4c} 177 � 15c‡Rb2SO4 �1435.6 �1317.0 197.4

�1435.07 � 0.60h�1316.91 � 0.59h 199.60 � 2.88h

�1316.806a§Cs2S �360.0 �348 � 9c† 178 � 15c‡

148.1b

163 � 30 averageCs2SO �622 � 24c§ �587 � 25c} 185 � 15c‡Cs2SO2 �890 � 24c§ –826 � 25c} 193 � 15c‡Cs2SO3 �1134.7 �1042� 4c} 200 � 15c‡Cs2SO4 �1443.0 �1323.7 211.9

�1323.544a§ 200 � 15c‡Cs2S2O5 �1561.1 – –

Figure 2Plots of �fH

o(NaClOx,c)/kJ mol�1 (x = 0, 2, 3, 4) (upper plot) and�fH

o(KClOx,c)/kJ mol�1 (x = 0, 3, 4) (lower plot) as ordinate versus x asthe abscissa, illustrating the irregular variation typically found with x formost oxysalts. The value for �fH

o(KClO2,c) is unknown. No values arerecorded, of course, for (hypothetical) �fH

o(NaClO,c) or �fHo(KClO,c).

Table 2 (continued)

Compound �fHo (kJ mol�1) �fG

o (kJ mol�1) So298 (J K�1 mol�1)

Selenium compoundsNa2Se �341.4 �339.9 129.8

123 � 15c‡Na2SeO2 �800.5c§ �738 � 4c} 131 � 15c‡Na2SeO3 �958.6 �865 � 4c} 129 � 15c‡Na2SeO4 �1069.0 �941.7 117.7g

148� 15c‡SeO2 �225.35a

�171.471a 66.693a

References: (a) Barin (1993); (b) Latimer (1961); (c) this work; (d) Lindberg et al. (2007);(e) O’Hare et al. (1986); (f) Cordfunke et al. (1987); (g) Karapet’yants & Karapet’yants(1970); (h) Palmer et al. (2002). † Indicates a Gibbs energy of formation value obtainedby first estimating �fS

o using the averaged standard absolute entropy estimate and thencalculating �fG

o = �fHo� T�fS

o. ‡ Indicates the standard absolute entropy valueestimated using Jenkins & Glasser’s (2003) equation: S = kVm + c. § Indicates dataobtained via least-squares fits in Table 1. } Indicates a Gibbs energy of formation valueobtained by first estimating �fS

o using the standard absolute entropy estimate and thencalculating �fG

o = �fHo� T�fS

o.

situation, shown for chlorine oxy salts, is typical and is found in

the case of oxy salts derived from almost every element in the

periodic table.

In stark contrast, in the unique case of the element sulfur, a

different scenario emerges. In the case of the oxy salts M2SOx

and M2S2Ox (x < 8), where M = alkali metal data (Wagman et

al., 1982; Karapet’yants & Karapet’yants, 1970; Barin, 1993),

such as �fHo or �fG

o as a function of x result in linear plots –

possessing correlation coefficients each in excess of R2 = 0.990.

Plots can be made for �fHo(Li2SOx,c) (x = 0, 3, 4; Table 1, item

1), �fHo(Na2SOx,c) (x = 0, 3, 4; Table 1, item 2),

�fGo(Na2SOx,c) (x = 0, 3, 4; Table 1, item 3), �fH

o(Na2S2Ox,c)

(x = 0, 3–7; Table 1, item 4), �fGo(Na2S2Ox,c) (x = 0, 3, 6, 7;

Table 1, item 5), �fHo(K2SOx,c) (x = 0, 3, 4; Table 1, item 6),

�fGo(K2SOx,c) (x = 0, 4; Table 1, item 7), �fH

o(K2S2Ox,c) (x =

0, 3, 5, 6; Table 1, item 8), �fHo(Rb2SOx,c) (x = 0, 4; Table 1,

item 9) and �fHo(Cs2SOx,c) (x = 0, 3, 4; Table 1, item 10). No

plots can be made for �fGo(Li2SOx,c), �fH

o(Li2S2Ox,c),

�fGo(Li2S2Ox,c), �fG

o(K2S2Ox,c), �fGo(Rb2SOx,c),

�fHo(Rb2S2Ox,c), �fG

o(Rb2S2Ox,c). In the plots for

�fGo(K2SOx,c)(x = 0, 4; Table 1 item 7) and

�fHo(Rb2SOx,c)(x = 0, 4; Table 1 item 9) only two data points

are available and so linearity is assumed and therefore R2 =

1.00. Errors are estimated from the agreement shown between

known experimental data and the estimated data given by

regression equations, the square root of the sums of the

squares of the errors found for M2S and for M2SO3 is used as

an estimate for the error when interpolating values for M2SO

and M2SO2 (this is cited in Table 1, column 8). For the

compounds M2S2Ox an overall sum-of-squares error is quoted.

These observations make two things possible:

(i) It enables estimation of thermochemical data for well

established salts merely by interpolation.

(ii) It also enables us to estimate data for hypothetical, and

as yet unprepared compounds, examples being the thioper-

oxides, M2SO (x = 1), and the sulfoxylates, M2SO2 (x = 2),

since the data lie on (almost) perfect straight lines. This data

can then be used to gain information on potential synthetic

routes to these new materials.

Table 1 shows the rectilinear regression fits that can be

made in cases where sufficient data exists in Table 2 to provide

the listed plots. Table 2 lists all the known thermochemical

data (Wagman et al., 1982; Karapet’yants & Karapet’yants,

1970; Barin 1993) at 298 K and pressure 101 325 Pa for two

separate families of alkali metal sulfur compounds, M2SOx and

M2S2Ox. Table 2 summarizes the established experimental

(upright type) and estimated (italic type) data assembled in

this study.

Typical plots are illustrated in Fig. 3 for �fHo(Na2SOx,c)

and �fHo(Na2S2Ox,c) versus x; in Fig. 4 for �fH

o(K2SOx,c) and

�fHo(K2S2Ox,c) versus x and in Fig. 5 for �fG

o(Na2SOx,c) and

�fGo(Na2S2Ox,c) versus x.

It is not possible to establish an analogous plot to Fig. 5 for

K+ salts simply because the majority of the data available in

Wagman et al. (1982) is for aqueous salts (not the subject of

this paper). It should be acknowledged that the only observed

deviation from strict linearity occurs with the �fHo data (x >

7) for the salt K2S2O8 which lies above (by 290 kJ mol�1) the

plot for the remaining salts containing less than eight O atoms.

It is worthwhile noting, with respect to this compound, that the

crystal structure determination is an old one, dating from 1935

and made using oscillating photographs. This data point has

been excluded when fitting the analytical form for the data.

The existence of such simple plots makes the interpolation

of missing data for these compounds straightforward with a

high likelihood of being reasonably accurate.

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o(K2S2Ox,c)/kJ mol�1 (x = 0, 3, 4, 5, 6, 7) as ordinate versus xas the abscissa (dotted line), and �fH

o(K2SOx,c)/kJ mol�1 (x = 0, 4, 5, 6)as ordinate versus x as the abscissa (solid line). Data from Table 2. Least-squares fitted lines take the forms: �fH

o(K2S2Ox,c)/kJ mol�1’ �218.4x

� 459.2 for which R2 = 0.997, N = 5 (item 8), �fHo(K2SOx,c)/kJ mol�1

’

�260.6x �373.3 for which R2 = 0.998, N = 3 (item 6).


o(Na2S2Ox,c)/kJ mol�1 (x = 0, 3, 4, 5, 6, 7) as the ordinateversus x as the abscissa (dotted line), and �fH

o(Na2SOx,c)/kJ mol�1 (x =0, 3, 4) as the ordinate versus x as the abscissa (solid line). Data fromTable 2. Least-squares fitted lines take the forms: �fH

o(Na2S2Ox,c)/kJ mol�1

’ �215.1x �413.0 for which R2 = 0.996, N = 6 (item 4),�fH

o(Na2SOx,c)/kJ mol�1’ �253.2x �360.1 for which R2 = 0.999, N = 3

(item 2).

3. Currently unavailable thermodynamic data for wellestablished compounds estimated by interpolation

3.1. Polysulfide oxyanion salts

3.1.1. Enthalpies of formation. We can use the correlation

(item 8) summarized in Table 1 to predict the standard

enthalpy of formation of dipotassium dithionite, K2S2O4. The

result is given in Table 2.

3.1.2. Gibbs energy of formation. We use the correlations

(item 5) from Table 1 to predict the standard Gibbs energy of

formation of disodium metabisulfite (pyrosulfite), Na2S2O5.

The result is given (in italics) in Table 2.

4. Currently unavailable thermodynamic data forhypothetical salts estimated by interpolation

4.1. Thioperoxides, M2SO

4.1.1. Enthalpies of formation. Interpolation of the linear

plots of �fHo(M2SOx,c) versus x (items 1, 2, 6, 9 and 10 in

Table 1) for x = 1 leads to the predicted data for Li2SO, Na2SO,

K2SO, Rb2SO and Cs2SO given (in italics) in Table 2.

4.1.2. Gibbs energies of formation. The complete absence

(see Table 2) of any �fGo data for Li salts and the existence of

only aqueous data (Wagman et al., 1982) for both Rb and Cs

salts [with the exception of single values for �fGo(Rb2SO4,c)

and �fGo(Cs2SO4,c)] prevent the construction of

�fGo(M2SOx,c) versus x correspondence plots for these alkali

metals so no data for Li2SO, Rb2SO or Cs2SO can be

predicted. However, in the case of the disodium and dipo-

tassium salts we interpolate (items 3 and 7 in Table 1) the data

listed (in italics) in Table 2.

4.2. Sulfoxylates, M2SO2 (x = 2)

4.2.1. Enthalpies of formation. Interpolation of the linear

plots of �fHo (M2SOx,c) versus x (items 1, 2, 6, 9 and 10 in

Table 1) for x = 2 lead to the predicted data for Li2SO2,

Na2SO2, K2SO2, Rb2SO2 and Cs2SO2 (in italics) in Table 2.

4.2.2. Gibbs energies of formation. For the case of the

disodium and dipotassium sulfoxylate salts we find (items 3

and 7 in Table 1) the data listed (in italics) in Table 2.

5. Previous thermodynamics

Previously, the only reference in the literature related to the

thermodynamic parameters of alkali metal thioperoxides,

M2SO, and sulfoxylates, M2SO2, was embodied in two publi-

cations (Ponikvar & Liebman, 2004; Toscano et al., 2003)

dealing with aqueous species. Jenkins & Tudela (2003) studied

the question of the stability of bisulfites. Although the bisul-

fites, MHSO3 (M = Li, Na, and K), were widely believed to be

stable compounds, they have never been obtained as solids. It

appeared that the cations, M+ are insufficiently large enough

to stabilize the HSO�3 ion relative to the metabisulfite, S2O2�5 ,

ion. These compounds (MHSO3) have had a chequered

history. Crystalline compounds, originally thought to be

NaHSO3 and KHSO3, were identified by Foerster et al. (1924)

to be metabisulfites, Na2S2O5 and K2S2O5. Simon & Schmidt

(1960) reported the synthesis of MHSO3 salts (M = Rb and

Cs), but the contention that these salts contained HSO�3anions was challenged (Schmidt & Wirwoll, 1960) because

they failed to react with disulfur dichloride in anhydrous

tetrahydrofuran to form HCl and M2S4O6. It was two decades

before Meyer et al. (1979) provided convincing spectroscopic

evidence for the presence of HSO�3 , so establishing the salts as

being RbHSO3 and CsHSO3. The fact that RbHSO3 and

CsHSO3 can be isolated, whilst attempts to crystallize MHSO3

(M = Li, Na, K) led to the formation of M2S2O5 (Jenkins et al.,

1999) [2MHSO3 (s) ! M2S2O5(s) + H2O(l)] was explained

using VBT (Jenkins & Tudela, 2003). Some additional ther-

modynamic data supplied by one of our reviewers is incor-

porated into Table 2.

6. Predicted thermodynamic values for DfHo and DfG

o

for thiosulfoxylate, M2S2O, and dithiosulfoxylate,M2S2O2, salts

Interpolated values of:

�fHo (items 4 and 8, Table 1, x = 1) and �fG

o (item 5, Table

1, x = 1) are listed in Table 2 for thiosulfoxylates.

�fHo (items 4 and 8, Table 1, x = 2) and �fG

o (item 5, Table

1, x = 2) are listed (in italics) in Table 2 for dithiosulfoxylates.

7. Estimation of So298(M2SO,c) and So298(M2SO2,c) forremaining salts using VBT

In Table 2 this work has established data (in italics) for

�fGo(M2SO,c), �fG

o(M2SO2,c) (Table 1, items 3 and 7),

�fHo(M2SO,c) and �fH

o(M2SO2,c) (Table 1, items 2 and 6)

for M = Na and K and for �fHo(M2SO,c) and for

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Figure 5Plots of �fG

o(Na2S2Ox,c)/kJ mol�1 (x = 0, 3, 7) as ordinate versus x as theabscissa (dotted line) and �fG

o(Na2SOx,c)/kJ mol�1 (x = 0, 3, 4) asordinate versus x as the abscissa (solid line). Data from Table 2. Least-squares fitted lines take the forms: �fG

o(Na2S2Ox,c)/kJ mol�1’ �189.6x

� 406.9 for which R2 = 0.997, N = 4 (item 5), �fGo(Na2SOx,c)/kJ mol�1

’

�228.0x � 345.6 for which R2 = 0.999, N = 3 (item 3).

�fHo(M2SO2,c) (Table 1, items 1, 9 and 10) for M = Li, Rb and

Cs. What is required to do next is to estimate �fGo(M2SO,c)

and �fGo(M2SO2,c) for M = Li, Rb and Cs first by estimating

So298(M2SO,c) and So

298(M2SO2,c) and then by estimating

�fSo(M2SO,c) and �fS

o(M2SO2,c).

Experimental standard entropy data is only available in

Table 2 for the crystalline sulfates of Li, Rb and Cs (i.e. only

for x = 4) and so no plots similar to those made in Table 1 for

other alkali halide salts can be made here.

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Table 3Crystal structure volume data for M2SOx and M2SeOx salts (x = 0, 3, 4) in nm3 and estimated volumes for M2SO2 and M2SeO2 in nm3 based on theisomegethic rules.

Rules: Vm(M2SOx) (nm3)’ (1� x/y)Vm(M2S) + (x/y)Vm(M2SOy) and Vm(Na2SeOx) (nm3)’ (1� x/y)Vm(Na2Se) + (x/y)Vm(Na2SeOy); y = 1, 2, 3 and 4, but y 6¼ x.Estimated standard absolute entropies, S0

298(M2SOx,c) (J K�1mol�1) and S0298(Na2SeOx,c) (J K�1 mol�1) for x = 1 and 2, using the Jenkins Glasser equation.

No. of Oatomsin anion, x Vm(Li2SOx,s) (nm3) Vm(Na2SOx,s) (nm3) Vm(K2SOx,s) (nm3) Vm(Rb2SOx,s) (nm3) Vm(Cs2SOx,s) (nm3)

Sulfoxylates0 Li2S Na2S K2S Rb2S Cs2S

Cubic Cubic Cubic Cubic OrthorhombicFm�33m, Z = 4 Fm�33m, Z = 4 Fm�33m, Z = 4 Fm�33m, Z = 4 Pnma, Z = 4a = 0.5708 nm a = 0.6538 nm a = 0.7405 nm a = 0.765 nm a = 0.5383 nmVm = 0.0464 nm3 Vm = 0.0698 nm3 Vm = 0.1010 nm3 Vm = 0.1119 nm3 b = 0.8571 nmS0

298(Li2S,c) = 78 � 15(J K�1mol�1)

S0298(Na2S,c) = 109 � 15

(J K�1mol�1)S0

298(K2S,c) = 152 � 15(J K�1 mol�1)

S0298(Rb2S,c) = 167 � 15(J K�1 mol�1)

c = 1.039 nmVm = 0.1198 nm3

Na2S�5H2O S0298(Cs2S,c) = 178 � 15(J K�1 mol�1)Cmcm; Z = 4

V = 0.7052 nm3

Vm = 0.1763 nm3

Na2S�9H2OP4122; Z = 4V = 1.1132 nm3

Vm = 0.2783 nm3

1 Estimatedvolumes

Li2SO Na2SO K2SO Rb2SO Cs2SO12Vm(Li2S) + 1

2Vm(Li2SO2)= 0.0553 nm3

12Vm(Na2S) + 1

2Vm(Na2SO2)= 0.0738 nm3

12Vm(K2S) + 1

2Vm(K2SO2)= 0.1024 nm3

12Vm(Rb2S) + 1

2Vm(Rb2SO2)= 0.1144 nm3

12Vm(Cs2S) + 1

2Vm(Cs2SO2)= 0.1253 nm3

23Vm(Li2S) + 1

3Vm(Li2SO3)= 0.0553 nm3

23Vm(Na2S) + 1

3Vm(Na2SO3)= 0.0731 nm3

23Vm(K2S) + 1

3Vm(K2SO3)= 0.1025 nm3

23Vm(Rb2S) + 1

3Vm(Rb2SO3)= 0.1147 nm3

23Vm(Cs2S) + 1

3Vm(Cs2SO3)= 0.1253 nm3

34Vm(Li2S) + 1

4Vm(Li2SO4)= 0.0553 nm3

34Vm(Na2S) + 1

4Vm(Na2SO4)= 0.0745 nm3

34Vm(K2S) + 1

4Vm(Ka2SO4)= 0.1023 nm3

34Vm(Rb2S) + 1

4Vm(Rb2SO4)= 0.1144 nm3

34Vm(Cs2S) + 1

4Vm(Cs2SO4)= 0.1253 nm3

Average = 0.0553 nm3 Average = 0.0738 nm3 Average = 0.1024 nm3 Average = 0.1145 nm3 Average = 0.1253 nm3

S0298(Li2SO,c) = 90.2 � 15(J K�1 mol�1)

S0298(Na2SO,c) = 115.4 � 15

(J K�1mol�1)S0

298(K2SO,c) = 154.3 � 15(J K�1 mol�1)

S0298(Rb2SO,c) = 170.7 � 15(J K�1 mol�1)

S0298(Cs2SO,c) = 185.4 � 15(J K�1 mol�1)

2 Estimatedvolumes

Li2SO2 Na2SO2 K2SO2 Rb2SO2 Cs2SO212Vm(Li2S) + 1

2Vm(Li2SO4)= 0.0642 nm3

13Vm(Na2S) + 2

3Vm(Na2SO3)= 0 0765 nm3

13Vm(K2S) + 2

3Vm(K2SO3)= 0.1040 nm3

13Vm(Rb2S) + 1

2Vm(Rb2SO4)= 0.1168 nm3

12Vm(Cs2S) + 1

2Vm(Cs2SO4)= 0.1308 nm3

13Vm(Li2S) + 2

3Vm(Li2SO3)= 0.0641 nm3

12Vm(Na2S) + 1

2Vm(Na2SO4)= 0.0792 nm3

12Vm(K2S) + 1

2Vm(K2SO4)= 0.1036 nm3

S0298(Rb2SO2,c) = 173.8 �15a (J K�1 mol�1)

S0298(Cs2SO2,c) = 192.9 �15a (J K�1 mol�1)

2/5Vm(Li2S) +2/5Vm(Li2SO3) +1/5Vm(Li2SO4)= 0.0641 nm3

2/5Vm(Na2S) +2/5Vm (Na 2SO3) +1/5Vm(Na2SO4)= 0.0776 nm3

2/5Vm(K2S) + 2/5Vm(K2SO3) +1/5Vm(K2SO4)= 0.1038 nm3

Average = 0.0641 nm3 Average = 0.0778 nm3 Average = 0.1038 nm3

S0298(Li2SO2,c) = 102.2 �15 (J K�1 mol�1)

S0298(Na2SO2,c) = 120.8 �

15 (J K�1 mol�1)S0

298(K2SO2,c) = 156.2 �15 (J K�1 mol�1)

3 Li2SO3 Na2SO3 K2SO3 Rb2SO3 Cs2SO312Vm(Li2SO2) + 1

2Vm(Li2SO4)= 0.0731 nm3

Trigonal Trigonal 12Vm(Rb2SO2) +

12Vm(Rb2SO4)= 0.1192 nm3

12Vm(Cs2SO2) +

12Vm(Cs2SO4)= 0.1363 nm3

P�33, Z = 2 P�33m1, Z = 214Vm(Li2S) + 3

4Vm(Li2SO4)= 0.0730 nm3

a = 0.5459 nm a = 0.5915 nmc = 0.6179 nm c = 0.6968 A 1

4Vm(Rb2S) + 34Vm(Rb2SO4)

= 0.1192 nm3

14Vm(Cs2S) + 3

4Vm(Cs2SO4)= 0.1363 nm33/2Vm(Li2SO2)� 1

2Vm(Li2S)= 0.0731 nm3

Vm = 0.0798 nm3 Vm = 0.1055 nm3

S0298(Na2SO3,c)= 123.5 � 15

(J K�1 mol�1)

S0298(K2SO3,c)

= 158.5 � 15(J K�1 mol�1)

3/2Vm(Rb2SO2) �12Vm(Rb2S)= 0.1193 nm3

3/2Vm(Cs2SO2) �12Vm(Cs2S)= 0.1363 nm3

3Vm(Li2SO) � 2Vm(Li2S)= 0.0728 nm3

Average = 0.0730 nm3 3Vm(Rb2SO) � 2Vm(Rb2S)= 0.1194 nm3

3Vm(Cs2SO) � 2Vm(Cs2S)= 0.1363 nm3Crystal structure not

reported Average = 0.1193 nm3 Average = 0.1363 nm3

S0298(Li2SO3,c) = 114� 15 (J K�1 mol�1)

Crystal structure notreported

Crystal structure notreported

S0298(Rb2SO3,c) = 177� 15 (J K�1 mol�1)

S0298(Cs2SO3,c) = 200� 15 (J K�1 mol�1)

We now employ VBT (Jenkins et al., 1999; Jenkins, 2008,

2009; Glasser & Jenkins, 2011b) in order to obtain an estimate

of standard entropies for the salts in question.

Table 3 assembles crystal structure data for volumes of

M2SOx salts (x = 0, 3, 4) from which, using three forms of the

isomegethic rule (Jenkins et al., 2004), we have, in general

VmðM2SOxÞ ’ ð1� x=yÞ � VmðM2SÞ þ x=y � VmðM2SOyÞ ð1Þ

for y = 1, 2, 3, 4, but with the restriction that y 6¼ x. Specifically

this means that

VmðM2SOÞ ’1

2VmðM2SÞ þ

1

2VmðM2SO2Þ ð2Þ

VmðM2SOÞ ’2

3VmðM2SÞ þ

1

3VmðM2SO3Þ ð3Þ

VmðM2SOÞ ’3

4VmðM2SÞ þ

1

4VmðM2SO4Þ ð4Þ

VmðM2SO2Þ ’ 2=5VmðM2SÞ þ 2=5VmðM2SO3Þ

þ 1=5VmðM2SO4Þ ð5Þ

VmðM2SO2Þ ’1

3VmðM2SÞ þ

2

3VmðM2SO3Þ ð6Þ

VmðM2SO2Þ ’1

2VmðM2SÞ þ

1

2VmðM2SO4Þ ð7Þ

leading via the Jenkins Glasser Entropy equation (Jenkins &

Glasser, 2003)

So298ðM2SOx; cÞ ’ kVmðM2SOx; cÞ þ c ðx ¼ 1; 2Þ; ð8Þ

where k (J K�1 mol�1 nm�3) = 1360 and c (J K�1 mol�1) = 15

leading to the values listed in Table 3.

The results for So298(Li2SO,c), So

298(Rb2SO,c), So298(Cs2SO,c),

So298(Li2SO2,c), So

298(Rb2SO2,c), So298(Cs2SO2,c),

So298(Li2SO3,c), So

298(Rb2SO3,c) and So298(Cs2SO3,c) are given

(in italics) in Table 2, which, in turn, when substituted into the

equations

�fSo298ðM2SO; cÞ ’ So

298ðM2SO; cÞ

� 2So298ðM; cÞ

� So298ðS; rhombic; cÞ

�1

2So

298ðO2; gÞ ð9Þ

�fSo298ðM2SO2; cÞ ’ So

298ðM2SO2; cÞ

� 2So298ðM; cÞ


� So298ðO2; gÞ ð10Þ

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Table 3 (continued)

No. of Oatomsin anion, x Vm(Li2SOx,s) (nm3) Vm(Na2SOx,s) (nm3) Vm(K2SOx,s) (nm3) Vm(Rb2SOx,s) (nm3) Vm(Cs2SOx,s) (nm3)

4 Li2SO4 Na2SO4 K2SO4 Rb2SO4 Cs2SO4

Monoclinic Orthorhombic Orthorhombic Orthorhombic OrthorhombicP21/c, Z = 4 Fddd, Z = 8 Pnma, Z = 4 Pnma, Z = 4 Pnma, Z = 4a = 0.845 nm a = 0.9821 nm a = 0.5723 nm a = 0.780 nm a = 0.625 nmb = 0.495 nm b = 1.2307 nm b = 0.9998 nm b = 1.040 nm b = 1.096 nmc = 0.821 nm c = 0.5862 nm c = 0.7421 nm c = 0.600 nm c = 0.828 nmVm = 0.0819 nm3 Vm = 0.0886 nm3 Vm = 0.1062 nm3 Vm = 0.1217 nm3 Vm = 0.1418 nm3

S0298(Li2SO4,c) = 126.4� 15 (J K�1 mol�1)

S0298(Na2SO4,c) = 135.5 �

15 (J K�1 mol�1)S0

298(K2SO4,c) = 159.4 �15 (J K�1 mol�1)

S0298(Rb2SO4,c) = 180.5 �15 (J K�1 mol�1)

S0298(Cs2SO4,c) = 207.8 �15 (J K�1 mol�1)

Li2SO4�H2O Na2SO4�10H2OP21; Z = 2 P121/c1, Z = 4V = 0.2073 V = 1.460 nm3

Vm = 0.1037 nm3 Vm = 0.3650 nm3

Pyroelectric

Sodium selenoxylatesNaSeOx Na2Se Na2SeO2 Na2SeO3 Na2SeO4 HT;

Antifluorite; Z = 4 12Vm(Na2Se) + 1

2Vm(Na2SeO4, RT)= 0.0886 nm3

P21/c; Z = 4 Pnma; Z = 4V = 0.3179 nm3 V = 0.3366 nm3 V = 0.3766 nm3

Vm = 0.0795 nm3 13Vm(Na2Se) + 2

3Vm(Na2SeO3)= 0.0826 nm3

Vm = 0.0842 nm3 Vm = 0.0942 nm3

S0298(Na2Se,c) = 123 � 15

(J K�1 mol�1)S0

298(Na2SeO3,c) = 129� 15 (J K�1 mol�1)

S0298(Na2SeO4,c) = 143� 15 (J K�1 mol�1)2/5Vm(Na2Se) + 2/5Vm(Na2SeO3) +

1/5Vm(Na2SeO4) = 0.0850 nm3 Na2SeO4 RTAverage = 0.0854 nm3 Fddd; Z= 8S0

298(Na2SeO2,c) = 131 � 15(J K�1mol�1)

V = 0.7804 nm3

Vm = 0.0976 nm3

S0298(Na2SeO4,c)= 148 � 15 (J K�1 mol�1)

�fSo298ðM2SO3; cÞ ’ So

298ðM2SO3; cÞ

� 2So298ðM; cÞ


� 3=2So298ðO2; gÞ ð11Þ

leads us to the estimates (in units of J K�1 mol�1 and with

errors of � 15 J K�1 mol�1): �fSo(Li2SO,c) ’ �102,

�fSo(Rb2SO,c) ’ �116, �fS

o(Cs2SO,c) ’ �119,

�fSo(Li2SO2,c) ’ �193, �fS

o(Rb2SO2,c) ’ �216,

�fSo(Cs2SO2,c) ’ �214, �fS

o(Li2SO3,c) ’ �284,

�fSo(Rb2SO3,c) ’ �377 and �fS

o(Cs2SO3,c) ’ �310.

By means of a simple calculation in the supplementary

material1 (xS.1) of this paper, we show that if there is an

uncertainty in the calculated value of So298(M2SOx,c) by say,

z% (possibly due to the use of our approximate equation to

estimate So298), then the propagated uncertainty in the value of

�fSo(M2SOx,c), say y%, is smaller, such that y << z.

Continuing our calculation

�fGo ¼ �fH

o � T�fSo ð12Þ

so that we estimate the �fGo values for the salts listed, as

given in Table 2.

No experimental values are listed in Table 1 for

�fGo(Rb2S,c) or �fG

o(Cs2S,c). To complete the data set we

estimate these here. Since (Jenkins et al., 1999) V(Rb+)/nm3 =

0.01386, V(Cs+)/nm3 = 0.01882 and V(S2�)/nm3 = 0.067 �

0.019, then So298(M2S)/J K�1 mol�1 can be estimated from the

sulfide equivalent of equation (8) and is given in Table 2.

Alternatively, we can use Latimer’s approach (Latimer, 1961),

using his Tables 87 and 90, which leads to values of So298(M2S)/

J K�1 mol�1, as listed in Table 2. The average of the latter two

values is also listed in Table 2. Since

�fSo298ðM2S; cÞ ’ So

298ðM2S; cÞ

� 2So298ðM; cÞ


’ So298ðM2S; cÞ

� 2So298ðM; cÞ � 32:1;

ð13Þ

then for M = Rb, �fSo298(Rb2S,c)’ �47� 15 J K�1 mol�1 and

for M = Cs, �fSo298(Cs2S,c) ’ �50 � 15 J K�1 mol�1 which

lead to the values for �fGo(Rb2S,c) and �fG

o(Cs2S,c) listed in

Table 2 via equation (12).

8. General remarks concerning prediction of synthesisusing thermodynamic considerations

Successful prediction, ahead of synthesis, of inorganic

compounds using thermodynamics is not too common an

occurrence in chemistry and may be regarded by some as

highly speculative and not, therefore, rightfully the subject of a

modern crystal chemistry journal. In defence of our decision

to explore this area (mainly in the supplementary material)

firstly we would argue that it does happen occasionally. Indeed

it was the topic of Bill Dasent’s excellent book (Dasent, 1965)

‘Non–Existent Compounds’ which sparked much exploratory

work. Secondly we would point to a study made by Finch,

Gates and Jenkins in a series of papers (Finch et al., 1980;

Jenkins et al., 1982, 1994; Finch et al., 1993; Jenkins et al., 1996)

of the thermodynamics of the PClþ4 and PCl�6 gaseous ions.

Their investigation of the likely stability of MPCl6 compounds

(M = alkali metal) and their prediction (ahead of synthesis)

that CsPCl6 would be the only stable alkali metal salt was

proven following the synthesis of this salt by Muir (1993), after

several abortive attempts at doing so. Recently Hao et al.

(2007), using energy-resolved, collision-induced, ion-beam

mass spectrometry, have determined experimentally

�fHo(PCl4

+, g) and the result agrees well with the theoretical

predictions made earlier (Jenkins et al., 1994, 1996). A similar

result for �fHo(PCl4

+, g) – again in agreement with the

experimentally determined value (Hao et al., 2007) – can be

generated very simply using VBT (Jenkins et al., 1999; Jenkins,

2008, 2009; Glasser & Jenkins, 2011b). This result goes a long

way to establishing credibility to this new genre of thermo-

dynamics which is employed in this paper.

Notable too was the success of VBT (Jenkins, 2009) and

more extended methods (Dixon et al., 2004) of predicting that

the highly publicized (Der Spiegel, Scientific American, etc.)

and potentially environmentally friendly rocket propellant,

N5N3 azide, was actually unpreparable.

Thirdly, we would point out that one of the more recent

advances that has made the examination of the thermo-

dynamics involved with new potential inorganic syntheses

easier, has been the development of the isomegethic principle

(Jenkins et al., 2004). This rule enables the estimation of

volumes for materials for which no crystal structure data or

density data has yet been reported and, used in conjunction

with VBT (Jenkins et al., 1999; Jenkins, 2008, 2009; Glasser &

Jenkins, 2011b), leads to the possibility of estimating otherwise

elusive thermodynamics. Indeed, this is a key principle, used in

the present paper, which permits us to explore the thermo-

dynamics of the thioperoxides and sulfoxylates. In view of

these earlier successes, we feel reasonably confident that

attempts to prepare disodium selenoxylate, Na2SeO2, the

compound on which attention is focused within this main

paper, will eventually prove successful. In discussing the

stability of inorganic materials, however, we have to add a

caveat, urge some caution, and recognize that a system can be

apparently stable thermodynamically and yet kinetic changes

may still be taking place, albeit slowly, in some cases, which

can prevent the formation of the target material.

9. Investigation of thermodynamic feasibility ofselected synthetic routes to obtain sulfoxylates, M2SO2

As mentioned above, Vegas (2000, 2011) and Vegas & Garcıa-

Baonza (2007) have suggested a possible anti-fluorite struc-

ture for Na2SO2 in which the S atoms would form the f.c.c.

array with the alkali metal atoms at the tetrahedral positions,

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1 Supplementary data for this paper are available from the IUCr electronicarchives (Reference: EB5016). Services for accessing these data are describedat the back of the journal.

just as found in Na2S itself. The problem arises that the

positions of the O atoms cannot be predicted so until a

suitable synthesis is achieved for this salt (or a suitable

analogue) and a crystal structure determination be performed,

his prediction cannot be tested. The reason being that the SO2

groups cannot be accommodated at the cell origin, as in the

fluorite-type Na2S, because that Wyckoff site lies on a three-

fold axis, a site symmetry that cannot be satisfied by a SO2

group unless the O atoms were located in a higher occupancy

site with a fractional occupancy factor (s.o.f. less than 1).

Another possibility is to lower the symmetry of the Na2SO2

structure until the SO2 groups can be located either at binary

axes or at mirror planes.

This does not prevent us estimating the thermodynamics

since the problem of having insufficiently detailed structural

information is circumvented by the use of VBT (Jenkins et al.,

1999; Jenkins, 2008, 2009; Glasser & Jenkins, 2011b), since

structural features are not required in this approach. However,

the motivation to study the compound remains.

We consider briefly here the possible synthesis of alkali

metal sulfoxylates, particularly of the disodium salt. Having

secured (see Table 2) estimates of �fGo(M2SO2,c) for M =

alkali metal we can now investigate the thermodynamics of

their reactions and comment on the likely feasibility of their

syntheses.

9.1. Synthesis of Na2SO2 from Na2O2 and rhombic sulfur

As has been mentioned above, the synthesis of Na2SO2 was

attempted by Jansen & Wiench – as reported by Wiench

(1975) – who tried to obtain the compound by heating diso-

dium peroxide with sulfur, in a sealed ampoule under vacuum.

Na2O2ðcÞ þ Sðrhombic; cÞ ! Na2SO2ðcÞ ð14Þ

At ambient temperatures we might predict thermo-

dynamically that this reaction (14) is favoured, since

�Goð14Þ ¼�fG

oðNa2SO2; cÞ

��fGoðNa2O2; cÞ

��fGoðS; rhombic;cÞ

¼ ð�802� 22Þ � ð�447:7Þ � ð0Þ kJ mol�1

¼ � 354� 22 kJ mol�1: ð15Þ

Data are taken from Wagman et al. (1982) and from

Karapet’yants & Karapet’yants (1970). This synthesis was,

however, not successful.

Preparation of the corresponding dipotassium-based

sulfoxylate by a similar route involves dipotassium peroxide,

K2O2, for which �fGo(K2O2,c)/kJ mol�1 = �428.5 (Barin,

1993) and forming K2SO2 as the target salt, the corresponding

reaction has �Go/kJ mol�1 = �406, and appears to be slightly

(ca 50 kJ mol�1) more thermodynamically favoured than

Na2SO2 formation.

9.2. Temperature dependence of the thermodynamics ofsynthesis of Na2SO2 from Na2O2 and S

In order to investigate behaviour at temperatures other

than 298 K of any of our proposed synthetic reactions we need

to know how �fGo(M2SO2,c) varies with temperature, T.

Essentially this means repeating the interpolation procedure

described earlier at other temperatures. Provided linear plots

are obtained at these other temperatures we can proceed as

before. Using available data (Barin, 1993) for �fGo(Na2S,c),

�fGo(Na2SO3,c) and �fG

o(Na2SO4,c) at temperatures

between 300 and 700 K, and plotting this against x, we do

indeed find linear behaviour with R2 consistently 0.998 or

0.999. Generalizing, the empirical results give

�fGoTðNa2SOx; cÞ=kJ mol�1

’ ½0:064ðT=KÞ � 239:0�x

þ ½0:1392ðT=KÞ � 415:7�

ð16Þ

for 300 < T/K < 700 and specifically for disodium sulfoxylate,

Na2SO2, when x = 2 this gives

�fGoTðNa2SO2; cÞ=kJ mol�1

’ ½0:2672ðT=KÞ � 893:6�; ð17Þ

which expresses the Gibbs energy of formation of the hypo-

thetical salt as a function of temperature, T (K).

Using equation (17) we can now write a temperature-

dependent equation for �Go for reaction (14) at any

temperature, provided we have the associated data for

�fGoT(Na2O2,c)/kJ mol�1 for the same temperature range. The

latter data when plotted against temperature, taking values at

300, 400, 500, 600 and 700 K (Barin, 1993) conforms to a linear

plot (R2 = 1, N = 5) and leads to

�fGoTðNa2O2; cÞ=kJ mol�1

’ ½0:2227ðT=KÞ � 516:5�; ð18Þ

whereupon for reaction (14)

�GoTð14Þ=kJ mol�1

’ ½0:2672ðT=KÞ

� 893:6� � ½0:2227ðT=KÞ � 516:5�

’ ½0:0445ðT=KÞ � 377:3�: ð19Þ

The rather low magnitude of the coefficient of the

temperature-dependent term in equation (19) suggests a weak

temperature dependence of �GTo(14), in that between 300 and

700 K we witness only a 9 kJ mol�1 change (from

�354 kJ mol�1 at 298 K to �345 kJ mol�1 at 700 K).

We have to conclude that other factors (see below) must

have prevented Jansen’s synthesis of Na2SO2 from disodium

peroxide and sulfur by route (14).

9.3. Alternative synthesis of Na2SO2 from Na metal andsulfur dioxide gas

We propose here that a preferable route to successful

synthesis might be by means of a low-temperature route.

Clearly we need a medium for the sodium, since interacting

gas directly with solid (however reactive) would create a

surface reaction. However dissolving sodium in liquid

ammonia would mean we could bubble SO2 gas through it and

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thermodynamics says this is a favourable reaction using the

analysis below. The reaction is

2Naðliquid ammoniaÞ þ SO2ðgÞ ! Na2SO2ðcÞ; ð20Þ

for which

�Goð20Þ ¼�fGoðNa2SO2; cÞ

� 2�fGoðNa; liquid ammoniaÞ

��fGoðSO2; gÞ

¼ ð�802� 9Þ


� ð�300:1Þ

¼ ½�502� 2�fGoðNa; liquid ammoniaÞ�

� 9 kJ mol�1: ð21Þ

The value of �fGo(Na, liquid ammonia) is not immediately

available. However, we can estimate �fHo(Na, liquid

ammonia) by extrapolating data for �fHo of Na in liquid NH3

at a variety of concentrations (see Fig. 6) to an infinite

ammonia concentration. This will then approximate closely to

�fHo(Na, liquid ammonia). We find

�fHoðNa; liquid ammoniaÞ=kJ mol�1

!�2:0: ð22Þ

This in turn means that �fGo(Na, liquid ammonia) is also

likely to be very small in magnitude and thus when inserted

into equation (21) will lead to

�Goð22Þ=kJ mol�1’ �502� 9; ð23Þ

and so we conclude that this present route is more thermo-

dynamically favoured than the previous route, in addition to

the fact that this synthetic route provides a suitable solvent

medium in which to carry out the synthesis.

10. Thermodynamic stability of disodium sulfoxylate,Na2SO2, and other sulfoxylates

10.1. Possible decomposition of sulfoxylates

Were a sulfoxylate, M2SO2, to be thermodynamically

unstable once synthesized, then the decomposition mode in

equation (24) represents what is probably the most likely

route for such instability. Such a route arises because the

corresponding alkali metal sulfide and sulfate salts are highly

stable materials. Thus, the reaction

2M2SO2ðcÞ ! M2SðcÞ þM2SO4ðcÞ ð24Þ

must be examined, for which �Go(24) is given by

�Goð24Þ ¼�fG

oðM2SO4; cÞ

þ�fGoðM2S; cÞ � 2�fG

oðM2SO2; cÞ: ð25Þ

Table 4 uses the estimated and experimental data from

Table 2 to probe the stability of the alkali metal sulfoxylates. If

�Go(24) > 0 the decomposition reaction for M2SO2 will not

proceed and the sulfoxylate will be thermodynamically stable;

if, however �Go(24) < 0 the decomposition reaction for

M2SO2 is likely and the sulfoxylate will then be thermo-

dynamically unstable and would disproportionate on synth-

esis; in the case where �Go(24) ’ 0 the sulfoxylate will have

knife-edge stability. As a further consideration we must also

bear in mind the uncertainties associated with the magnitude

of �Go(24) in each case. �Go(24) is given in column 5 of

Table 4.

10.2. Conclusions concerning sulfoxylate stabilities

The data in columns 2, 3, 4 and 5 of Table 4 do not follow

smooth variation as we progress down the series from Li to Cs.

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o(Na in n NH3)/kJ mol�1 versus n showing that extrapolationto infinite n (corresponding to pure liquid ammonia) gives a value for�fH

o(Na, liquid ammonia)/kJ mol�1 approximating to �2.00. Data fromNBS tables (Wagman et al., 1982).

Table 4Likely thermodynamic stability of M2SO2 salts.

Conclusion about stabilityM �fG

o(M2SO4,c) (kJ mol�1) �fGo(M2S,c) (kJ mol�1) �fG

o(M2SO2,c) (kJ mol�1) �fGo(24) (kJ mol�1) Likely error in �Go(24)(kJ mol�1)

Li �1321.8 �436.1 �878 � 9 +1.7 Li2SO2 exhibits borderline stability� 11

Na �1270.2 �349.8 �802 � 9 �16.0 Na2SO2 appears to be unstable� 13

K �1321.4 �364.0 �853 � 18 +20.6 Along with Cs2SO2, K2SO2

emerges as a stable salt � 25Rb �1317.0 �350 � 8 �833 � ? +0.9 Rb2SO2 exhibits borderline (knife-

edge) stability > 8Cs �1323.7 �348 � 8 �826 � 11 +19.7 Along with K2SO2, Cs2SO2

emerges as a stable salt � 17

It is largely for this reason that the resultant values for

�Go(24) are somewhat erratic. The value of �Go(24) for

Na2SO2, for example, seems oddly positive when all the other

alkali metal results are negative; the trends do not seem quite

as might be expected. However, a smooth variation for sodium

�fGo data within an alkali metal series is not, in fact, expected

as the collected data for various alkali metal salts in Table 5

illustrates. Given then that our data seems to conform to other

exhibited trends, we conclude:

(i) that Na2SO2 emerges as likely to be unstable towards

disproportionation to the sulfide and sulfate;

(ii) that whilst Li2SO2 and Rb2SO2 have precarious

borderline stabilities, potassium and dicesium sulfoxylates

appear to be the two salts most likely to be preparable and

stable;

(iii) that K2SO2 and Cs2SO2 emerge as the two salts most

likely to be preparable and stable;

(iv) that uncertainties found for �Go(24) (which are

particularly large for K2SO2 and for Cs2SO2) make these

assignments of stability tentative.

11. Disodium selenoxylate

11.1. Synthesis of Na2SeO2 from Na metal (in liquidammonia) and solid selenium dioxide

In view of the uncertainty concerning the instability of

disodium sulfoxylate, we need to consider the stability and

preparation of a suitable crystallographic alternative

compound in order to test our structural prediction. Disodium

selenoxylate, Na2SeO2, selenium being the Group 16 element

below sulfur, is such a suitable compound and it also appears

to have a number of thermodynamic/synthetic advantages

over Na2SO2 for the following reasons. Whereas SO2 is a gas,

SeO2 is a solid material which could be reacted more easily

with Na in liquid ammonia. So, practically, this might represent

a facile synthesis. �fGo(SeO2,c)/kJ mol�1 = �171.471 (Table

2) so that the reaction

2Naðliquid NH3; lÞ þ SeO2ðcÞ ! Na2SeO2ðcÞ ð26Þ

has a large and negative free energy change

�Goð26Þ ¼�fGoðNa2SeO2; cÞ ��fG

oðSeO2; cÞ


’ ð�738� 8Þ � ð�171:471Þ � ð�2Þ kJ mol�1

¼ � 563� 8 kJ mol�1: ð27Þ

Since �Go(29) < �Go(22) the Na2SeO2 preparation is even

more thermodynamically favoured than the corresponding one

for Na2SO2.

11.2. Synthesis of Na2SeO2 from Na metal and solid seleniumdioxide

Direct reaction of powdered SeO2 with sodium metal can

also present a favourable reaction

2NaðcÞ þ SeO2ðcÞ ! Na2SeO2ðcÞ ð28Þ

which has a large and negative free energy change

�Goð28Þ ¼�fG

oðNa2SeO2; cÞ ��fG

oðSeO2; cÞ

� 2�fGoðNa; cÞ

’ ð�738� 8Þ

� ð�171:471Þ � ð0Þ

¼ � 566� 8 kJ mol�1: ð29Þ

11.3. Synthesis of Na2SeO2 from sodium peroxide, Na2O2

and selenium

Although less practically useful as a preparative route (by

virtue of a surface reaction possibly slowing the kinetics) the

reaction of powdered selenium metal with sodium peroxide

Na2O2ðcÞ þ SeðcÞ ! Na2SeO2ðcÞ ð30Þ

also has a large and negative free energy change

�Goð30Þ ¼�fGoðNa2SeO2; cÞ

��fGoðNa2O2; cÞ

��fGoðSe; cÞ

’ ð�738:3� 8Þ � ð�447:7Þ � ð0Þ kJ mol�1

¼ � 303� 8 kJ mol�1: ð31Þ

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Table 5Variation of free energy data down an alkali metal series for selected salts (Wagman et al., 1982).

M �fGo(M2CO3,c) (kJ mol�1) �fG

o(M2O2,c) (kJ mol�1) �fGo(MH,c) (kJ mol�1) �fG

o(MNO3,c) (kJ mol�1) �fGo(MNO2,c) (kJ mol�1)

Li �1132.1 �571.0a�68.3 �381.1 �302.0

Na �1044.4 �447.7 �33.5 �367.0 �284.6K �1063.5 �425.1 �34.0a

�394.9 �306.6�428.5a

Rb �1051.0 � � �395.8 �306.2Cs � � � � �

References: (a) Barin (1993).

11.4. Thermodynamic stability of Na2SeO2

Finally, with regard to the stability of Na2SeO2 and its

possible disproportionation to selenide and selenate

2Na2SeO2ðcÞ ! Na2SeðcÞ þ Na2SeO4ðcÞ; ð32Þ

which is seen to be thermodynamically forbidden

�Goð32Þ ¼�fGoðNa2SeO4; cÞ

þ�fGoðNa2Se; cÞ

� 2�fGoðNa2SeO2; cÞ

’ ð�941:7Þ þ ð�339:9Þ � 2ð�738� 8Þ kJ mol�1

¼ þ 194� 11 kJ mol�1: ð33Þ

The high positive value of �Go(32) ensures the complete

stability of the target disodium selenoxylate, Na2SeO2.

11.5. Na2SeO2 from a crystallographic standpoint

The fact that it appears that we are likely to be able to

synthesize a stable Na2SeO2 prompts us to analyse the

detailed structures of other Na2SeOx (x = 3 and 4). At ambient

conditions Na2SeO4 is isostructural with thenardite (V-

Na2SO4) (Fddd) (Kalman & Cruickshank, 1970), but at high

temperature it transforms into the glasserite-type structure of

�-K2SO4 (Pnma) (Mehrotra et al., 1977). This phase transition

which occurs in sodium selenate has not been observed in the

corresponding sulfate, which transforms directly from

thenardite to I-Na2SO4 (P63/mmc). These phase changes are

summarized below (in Path 2) and as will be discussed later,

the cation subarrays of these structures correspond to TiSi2,

PbCl2 and Ni2In, respectively.

The structures of the two Na2SeO4 polymorphs are repre-

sented in Fig. 7.

The structure of selenite, Na2SeO3 (P21/c) (Wickleder,

2002), presents us with some peculiarities. If one tries to

describe it as a set of trigonal prisms like those existing in

Na2SO3 they are completely distorted and quite far from that

of Na2SO3 (cf. Figs. 8a and d). However, the structure is better

described as a distorted f.c.c. array formed by both Se and Na

atoms (see Fig. 8b), as shown by the distorted cubes repre-

sented in Fig. 8(c).

The important point to make is that in Na2SO3 the Na2S

moiety is compressed with respect to the CaF2-type structure

(Vegas, 2011). The Na atoms, as in the CaF2-type structure,

form a simple cubic network in which alternative cubes are

filled by F(S) atoms. In Na2SO3, however, all the cubes are

filled indistinctly by Na and SO3 groups (see Fig. 6e). Thus, Na

and S atoms altogether form a b.c.c.-type array. An important

aspect of this array is that the cubes filled with the SO3 groups

are in fact oxygen-stuffed Na8S cubes like those existing in the

fluorite structure (see Fig. 1a and Fig. 9a). This indicates that

Na2SO3 is close to the fluorite structure and that if the O

content is lowered, as in Na2SO2, the array should be even

closer to that of CaF2, as we have postulated.

In the heavier Na2SeO3 the Na and Se atoms together form

a f.c.c. structure (see Fig. 9c) which should be considered as

having a denser packing than is found in the sulfite. In both

cases, the result is as expected and yields cation arrays which

are closer to the parent CaF2-type structures of Na2S and

Na2Se (Vegas, 2011).

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Figure 7(a) The structure of room-temperature Na2SeO4 (Fddd), which is of thethenardite-type. (b) The high-temperature phase of Na2SeO4 (Pnma).The SeO4 tetrahedra lie at the centre of the Na6 trigonal prisms. Na:green; Se: yellow; O: red.

12. Concluding remarks

The provision of missing thermodynamic data for well estab-

lished polysulfur oxysalts has been readily established in this

paper relying on experimental data for M2S2Ox, where x is in

the range 0 � x � 7. The �fHo values established for thio-

peroxides and sulfoxylates in Table 2 rely on plots made where

0� x � 4 – a smaller compass of values than for the polysulfur

oxy salts – but nevertheless the plots are reliably linear. Only

�fGo values can robustly be established for the disodium and

dipotassium thioperoxides and sulfoxylates. The remaining

�fGo data, predicted for the Li, Rb and Cs salts, are less

certain since they rely on VBT approximate methods (Jenkins

et al., 1999; Jenkins, 2008, 2009; Glasser & Jenkins, 2011b) to

secure values.

The importance of the data provided in this paper is

threefold:

(i) It is established, in its own right, as an addition to the

(existing) thermochemical literature.

(ii) It further permits us to explore, on thermodynamic

grounds, the existence of compounds whose synthesis has not

yet been achieved and enables comment on their stabilities.

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Figure 8A comparison of the structure of Na2SeO3 with that of Na2SO3. (a) The structure of Na2SeO3 viewed along the a axis. Very distorted Na6 trigonal prismshave been drawn to be compared with the corresponding network in Na2SO3 as is represented in (d); Na: green; Se: yellow; O: red. (b) The same arrayshowing the f.c.c. packing formed by the Na and Se atoms altogether. (c) Two cubes showing the distorted f.c.c. cells. (d) The structure of Na2SO3 showingthe distorted trigonal Na6 prisms centred on the SO3 groups. The Na and S atoms form a Ni2Al-type structure. (e) The alternative description of thestructure consisting of slightly distorted Na8 cubes. Some of them are centred on Na atoms, others by SO3 groups. Na: violet; S: yellow; O: red.

(iii) Moreover, in the special case of the sulfoxylates and

selenoxylates, this work is additionally important because it

will provide a basis for the discussion in the following papers

which will be concerned with the possible synthesis of

sulfoxylates M2SO2 (M = K and Cs) and sodium selenoxylate

Na2SeO2, as well as a discussion of the relationship between

oxidation and pressure in these materials.

As has already been reported (Martınez-Cruz et al., 1994;

Vegas & Tranqui, 1996; Vegas, 2000, 2011; Vegas & Mattesini,

2010) the insertion of O atoms into the structure of an alloy

(here, the term alloy is applied to the M2S sulfides) should be

equivalent to the application of a physical pressure to the M2S

and M2Se subarrays from which the oxidized lattices have

been formed. This pressure should be proportional to the

number of O atoms inserted (Vegas & Garcıa-Baonza, 2007;

Vegas, 2011) in such a way that the M2S substructures of the

M2SOx sulfates would be expected to be related to the high-

pressure phases of the respective M2S sulfides.

Considering the alkali metal sulfides M2S (M = Li, Na, K,

Rb, Cs) together, the observed experimental trend is that their

structures undergo the transition path, denoted as Path 1 in x1,

by increasing pressure (Vegas, 2011), and are represented in

Fig. 9.

It should be remembered that the relationship between

oxidation and pressure – first expressed by Martınez-Cruz et

al. in 1995, and later confirmed in the high-pressure studies

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Table 6Equivalences found between the structures of M2S and those of the cation subarrays in their respective M2SOx.

These structure types are represented in Fig. 6.

CaF2 ! Ni2Al ! PbCl2 ! Ni2In ! TiSi2

Li2S High-pressure Li2SNa2S High-pressure Na2S High-pressure Na2SK2S High-pressure K2SRb2S High-pressure Rb2S High-pressure Rb2S– – Cs2S High-pressure Cs2S

High-temperature Li2SO4 Na2SO3 K2SO3 K2SO4 Cs2SO4 High-temperatureNa2SO4

Room-temperatureNa2SO4

High-temperature Cs2SO4 High-temperatureNa2SeO4

High-temperature K2SO4 Room-temperatureNa2SeO4 (thenardite)

Figure 9The different structures of Na2S withincreasing pressure. (a) The anti-CaF2 structurestable at ambient conditions. Compare with theproposed structure of Na2SO2 represented inFig. 1(b). (b) The Ni2Al-type structure of theNa2S subarray in Na2SO3 (Vegas, 2011). (c)The anti-PbCl2-type structure of Na2S at7.0 GPa. (d) The Ni2In-type structure of Na2Sat 16 GPa (Vegas et al., 2001). It is present inthe Na2S-subarray of the high-temperaturephase I-Na2SO4 (Rasmussen et al., 1996). (e)The TiSi2-type structure present in thenardite(V-Na2SO4).

carried out on the Li2S (Grzechnik et al., 2000), Na2S (Vegas et

al., 2001), K2S (Vegas et al., 2002), Rb2S (Santamaria-Perez et

al., 2011a), Cs2S (Santamarıa-Perez et al., 2011b) sulfides –

leads to the situation that in the corresponding M2SOx (M =

Li, Na, K, Rb, Cs) sulfates, the insertion of the O atoms

provokes a phase transition in their M2S substructures. The

expected structural change would lead to the situation where

in the oxides (sulfates) we should expect to find one (or more)

of these high-pressure phases adopted by the M2S sulfides.

That is, insertion of O atoms induces the stabilization of the

structures which are found in the high-pressure phases of the

alloy (in this case, M2S). The question as to which of the

phases as quoted in path 1 is stabilized in the oxide will depend

on the number of O atoms inserted in the sulfide

lattice.

Thus, in Table 6 we list the equivalences found between the

structures of M2S and those of the cation subarrays in their

respective M2SOx. Here, the data given are restricted to

sulfides, but should the whole of the chalcogenides be

compared, the relationships would become even more evident

(Vegas, 2011). Compare with the structures in Fig. 9.

Referring to Table 6 on increasing external pressure on the

lattice, the double transition: anti-fluorite (anti-CaF2)! anti-

PbCl2 ! Ni2In has been observed for Na2S (Vegas et al.,

2001). However, a complete analysis (Vegas, 2011) of the

transitions observed in both M2T and M2TOx (T = S, P, Si etc.)

compounds has also revealed a surprising parallelism between

both families of compounds which implies that the complete

structural transition path for Na2S might well be that quoted in

the top of Table 6.

The fact that the Ni2In-type structure is present in the high-

temperature (HT) phase of Na2SO4, and that the Na2S

subarray is of Ni2Al-type in Na2SO3, indicates that the CaF2-

type is likely to be the most probable structure for this same

subarray in the sulfoxylate, Na2SO2. The predicted structure is

drawn in Fig. 1. The known behaviour of the related Li2SO4,

K2SO4 and K2SO3 compounds further supports our predic-

tions. It is perhaps important to emphasize that the evolving

structures are either retaining their heavy-atom positions

[metal and sulfur] or provoking stabilization of the other high-

pressure structures whilst adding in additional O atoms.

Comparing Table 6 and Fig. 9 we can see that oxides and alloys

undergo the same phase transitions. Three factors influence

the structural changes, i.e. the O content (x), pressure and

temperature.

Thus, the phenakite-related structure of �-Li2SO4 becomes

anti-fluorite at high temperature. K2SO4 anti-PbCl2 under

ambient conditions, transforms into Ni2In-type at higher

temperatures and the sulfites K2SO3 and Na2SO3 are both of

the Ni2Al-type (Vegas, 2011; see Fig. 7). Both Na2SO4 and

Na2SeO4 are under ambient conditions of the TiSi2-type but

they transform at high temperatures into the Ni2In- and the

anti-PbCl2-types, respectively. As discussed above, for the

compounds Na2SO3 and Na2SeO3 the result is as expected,

that is, the lower O content corresponds to the production of

lower pressure, yielding cation arrays closer to the parent

CaF2-type structure of Na2S and Na2Se.

In connection with Vegas’ crystallographic studies

(Martınez-Cruz et al., 1994; Vegas & Martınez-Cruz, 1995;

Santamaria-Perez & Vegas, 2003; Santamaria-Perez et al.,

2005; Vegas, 2000, 2011; Vegas & Garcıa-Baonza, 2007; Vegas

et al., 2009), and from the experimental high-pressure work by

Marques et al. (2009), we are anxious to demonstrate the

antifluorite structure for the sulfoxylate salts. The thermo-

dynamic and volumetric data discussed in this paper will form

the basis of a VBC discussion (AV and HDBJ) of this work

and other work (AV) will report the outcome of the practical

synthesis planned.

Dr Javier Medrano (CIB, CSIC, Madrid) is thanked for his

kind assistance in redrawing Figs. 3, 4 and 5. Professor Jenkins

would like to acknowledge the support of the University of

Warwick for providing facilities to enable this work to be

undertaken. Dr Angel Vegas (Madrid) and Professors

Fernando Rey (Valencia) and Francisco Javier Manjon

(Valencia) and their colleagues are thanked for arranging and

supporting a visit to the Instituto de Tecnologıa Quımica

Valencia (UPV-CSIC), Espana by HDBJ. Professor Jenkins

thanks his colleagues: Dr Nathaniel W. Alcock, OBE, FSA, for

useful comments and Dr Diane Holland for advice on error

treatment. One of our reviewers kindly brought to our

attention some additional data for which we thank him/her

and another reviewer focused our attention on stability of the

sulfoxylates with respect to their individual corresponding

sulfide and sulfate. AV is thanked for introducing HDBJ to

Juan de Cabanilles’, Batalla Imperial de Quinto Tono as

played on the XVIIth Century Echeverrıa Orguel of Toledo’s

‘Santa Marıa’ Cathedral by Paulino Ortiz.

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